1 | |
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2 | #include <NTL/GF2X.h> |
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3 | #include <NTL/vec_long.h> |
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4 | |
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5 | #include <NTL/new.h> |
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6 | |
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7 | NTL_START_IMPL |
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8 | |
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9 | long GF2X::HexOutput = 0; |
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10 | |
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11 | |
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12 | void GF2X::SetMaxLength(long n) |
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13 | { |
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14 | if (n < 0) Error("GF2X::SetMaxLength: negative length"); |
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15 | if (NTL_OVERFLOW(n, 1, 0)) |
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16 | Error("GF2X::SetMaxLength: excessive length"); |
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17 | long w = (n + NTL_BITS_PER_LONG - 1)/NTL_BITS_PER_LONG; |
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18 | xrep.SetMaxLength(w); |
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19 | } |
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20 | |
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21 | GF2X::GF2X(INIT_SIZE_TYPE, long n) |
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22 | { |
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23 | SetMaxLength(n); |
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24 | } |
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25 | |
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26 | |
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27 | |
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28 | const GF2X& GF2X::zero() |
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29 | { |
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30 | static GF2X z; |
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31 | return z; |
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32 | } |
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33 | |
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34 | void GF2X::normalize() |
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35 | { |
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36 | long n; |
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37 | const _ntl_ulong *p; |
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38 | |
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39 | n = xrep.length(); |
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40 | if (n == 0) return; |
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41 | p = xrep.elts() + n; |
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42 | while (n > 0 && (*--p) == 0) { |
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43 | n--; |
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44 | } |
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45 | xrep.QuickSetLength(n); |
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46 | } |
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47 | |
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48 | long IsZero(const GF2X& a) |
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49 | { return a.xrep.length() == 0; } |
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50 | |
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51 | long IsOne(const GF2X& a) |
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52 | { return a.xrep.length() == 1 && a.xrep[0] == 1; } |
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53 | |
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54 | |
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55 | |
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56 | |
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57 | |
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58 | |
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59 | |
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60 | long IsX(const GF2X& a) |
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61 | { |
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62 | return a.xrep.length() == 1 && a.xrep[0] == 2; |
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63 | } |
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64 | |
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65 | GF2 coeff(const GF2X& a, long i) |
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66 | { |
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67 | if (i < 0) return to_GF2(0); |
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68 | long wi = i/NTL_BITS_PER_LONG; |
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69 | if (wi >= a.xrep.length()) return to_GF2(0); |
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70 | long bi = i - wi*NTL_BITS_PER_LONG; |
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71 | |
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72 | return to_GF2((a.xrep[wi] & (1UL << bi)) != 0); |
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73 | } |
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74 | |
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75 | GF2 LeadCoeff(const GF2X& a) |
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76 | { |
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77 | if (IsZero(a)) |
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78 | return to_GF2(0); |
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79 | else |
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80 | return to_GF2(1); |
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81 | } |
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82 | |
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83 | GF2 ConstTerm(const GF2X& a) |
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84 | { |
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85 | if (IsZero(a)) |
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86 | return to_GF2(0); |
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87 | else |
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88 | return to_GF2((a.xrep[0] & 1) != 0); |
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89 | } |
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90 | |
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91 | |
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92 | void set(GF2X& x) |
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93 | { |
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94 | x.xrep.SetLength(1); |
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95 | x.xrep[0] = 1; |
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96 | } |
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97 | |
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98 | void SetX(GF2X& x) |
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99 | { |
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100 | x.xrep.SetLength(1); |
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101 | x.xrep[0] = 2; |
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102 | } |
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103 | |
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104 | void SetCoeff(GF2X& x, long i) |
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105 | { |
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106 | if (i < 0) { |
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107 | Error("SetCoeff: negative index"); |
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108 | return; |
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109 | } |
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110 | |
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111 | long n, j; |
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112 | |
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113 | n = x.xrep.length(); |
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114 | long wi = i/NTL_BITS_PER_LONG; |
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115 | |
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116 | if (wi >= n) { |
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117 | x.xrep.SetLength(wi+1); |
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118 | for (j = n; j <= wi; j++) |
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119 | x.xrep[j] = 0; |
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120 | } |
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121 | |
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122 | long bi = i - wi*NTL_BITS_PER_LONG; |
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123 | |
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124 | x.xrep[wi] |= (1UL << bi); |
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125 | } |
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126 | |
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127 | |
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128 | |
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129 | void SetCoeff(GF2X& x, long i, long val) |
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130 | { |
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131 | if (i < 0) { |
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132 | Error("SetCoeff: negative index"); |
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133 | return; |
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134 | } |
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135 | |
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136 | val = val & 1; |
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137 | |
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138 | if (val) { |
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139 | SetCoeff(x, i); |
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140 | return; |
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141 | } |
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142 | |
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143 | // we want to clear position i |
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144 | |
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145 | long n; |
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146 | |
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147 | n = x.xrep.length(); |
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148 | long wi = i/NTL_BITS_PER_LONG; |
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149 | |
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150 | if (wi >= n) |
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151 | return; |
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152 | |
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153 | long bi = i - wi*NTL_BITS_PER_LONG; |
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154 | |
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155 | x.xrep[wi] &= ~(1UL << bi); |
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156 | if (wi == n-1) x.normalize(); |
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157 | } |
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158 | |
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159 | void SetCoeff(GF2X& x, long i, GF2 a) |
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160 | { |
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161 | SetCoeff(x, i, rep(a)); |
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162 | } |
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163 | |
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164 | |
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165 | void swap(GF2X& a, GF2X& b) |
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166 | { |
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167 | swap(a.xrep, b.xrep); |
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168 | } |
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169 | |
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170 | |
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171 | |
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172 | long deg(const GF2X& aa) |
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173 | { |
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174 | long n = aa.xrep.length(); |
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175 | |
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176 | if (n == 0) |
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177 | return -1; |
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178 | |
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179 | _ntl_ulong a = aa.xrep[n-1]; |
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180 | long i = 0; |
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181 | |
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182 | if (a == 0) Error("GF2X: unnormalized polynomial detected in deg"); |
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183 | |
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184 | while (a>=256) |
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185 | i += 8, a >>= 8; |
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186 | if (a >=16) |
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187 | i += 4, a >>= 4; |
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188 | if (a >= 4) |
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189 | i += 2, a >>= 2; |
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190 | if (a >= 2) |
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191 | i += 2; |
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192 | else if (a >= 1) |
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193 | i++; |
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194 | |
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195 | return NTL_BITS_PER_LONG*(n-1) + i - 1; |
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196 | } |
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197 | |
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198 | |
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199 | long operator==(const GF2X& a, const GF2X& b) |
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200 | { |
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201 | return a.xrep == b.xrep; |
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202 | } |
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203 | |
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204 | long operator==(const GF2X& a, long b) |
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205 | { |
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206 | if (b & 1) |
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207 | return IsOne(a); |
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208 | else |
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209 | return IsZero(a); |
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210 | } |
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211 | |
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212 | long operator==(const GF2X& a, GF2 b) |
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213 | { |
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214 | if (b == 1) |
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215 | return IsOne(a); |
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216 | else |
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217 | return IsZero(a); |
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218 | } |
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219 | |
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220 | void random(GF2X& x, long n) |
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221 | { |
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222 | if (n < 0) Error("GF2X random: negative length"); |
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223 | |
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224 | if (NTL_OVERFLOW(n, 1, 0)) |
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225 | Error("GF2X random: excessive length"); |
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226 | |
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227 | long wl = (n+NTL_BITS_PER_LONG-1)/NTL_BITS_PER_LONG; |
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228 | |
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229 | x.xrep.SetLength(wl); |
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230 | |
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231 | long i; |
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232 | for (i = 0; i < wl-1; i++) { |
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233 | x.xrep[i] = RandomWord(); |
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234 | } |
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235 | |
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236 | if (n > 0) { |
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237 | long pos = n % NTL_BITS_PER_LONG; |
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238 | if (pos == 0) pos = NTL_BITS_PER_LONG; |
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239 | x.xrep[wl-1] = RandomBits_ulong(pos); |
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240 | } |
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241 | |
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242 | x.normalize(); |
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243 | } |
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244 | |
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245 | void add(GF2X& x, const GF2X& a, const GF2X& b) |
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246 | { |
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247 | long sa = a.xrep.length(); |
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248 | long sb = b.xrep.length(); |
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249 | |
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250 | long i; |
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251 | |
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252 | if (sa == sb) { |
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253 | x.xrep.SetLength(sa); |
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254 | if (sa == 0) return; |
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255 | |
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256 | _ntl_ulong *xp = x.xrep.elts(); |
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257 | const _ntl_ulong *ap = a.xrep.elts(); |
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258 | const _ntl_ulong *bp = b.xrep.elts(); |
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259 | |
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260 | for (i = 0; i < sa; i++) |
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261 | xp[i] = ap[i] ^ bp[i]; |
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262 | |
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263 | i = sa-1; |
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264 | while (i >= 0 && !xp[i]) i--; |
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265 | x.xrep.QuickSetLength(i+1); |
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266 | } |
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267 | |
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268 | else if (sa < sb) { |
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269 | x.xrep.SetLength(sb); |
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270 | _ntl_ulong *xp = x.xrep.elts(); |
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271 | const _ntl_ulong *ap = a.xrep.elts(); |
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272 | const _ntl_ulong *bp = b.xrep.elts(); |
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273 | |
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274 | for (i = 0; i < sa; i++) |
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275 | xp[i] = ap[i] ^ bp[i]; |
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276 | |
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277 | for (; i < sb; i++) |
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278 | xp[i] = bp[i]; |
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279 | } |
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280 | else { // sa > sb |
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281 | x.xrep.SetLength(sa); |
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282 | _ntl_ulong *xp = x.xrep.elts(); |
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283 | const _ntl_ulong *ap = a.xrep.elts(); |
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284 | const _ntl_ulong *bp = b.xrep.elts(); |
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285 | |
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286 | for (i = 0; i < sb; i++) |
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287 | xp[i] = ap[i] ^ bp[i]; |
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288 | |
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289 | for (; i < sa; i++) |
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290 | xp[i] = ap[i]; |
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291 | } |
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292 | } |
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293 | |
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294 | |
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295 | |
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296 | |
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297 | |
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298 | /* |
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299 | * The bodies of mul1, Mul1, AddMul1, and mul_half |
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300 | * are generated by the MakeDesc program, and the |
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301 | * macros NTL_BB_MUL_CODE... are defined in mach_desc.h. |
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302 | * Thanks to Paul Zimmermann for providing improvements |
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303 | * to this approach. |
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304 | */ |
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305 | |
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306 | |
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307 | #if (defined(NTL_GF2X_ALTCODE1)) |
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308 | |
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309 | #define NTL_EFF_BB_MUL_CODE0 NTL_ALT1_BB_MUL_CODE0 |
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310 | #define NTL_EFF_BB_MUL_CODE1 NTL_ALT1_BB_MUL_CODE1 |
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311 | #define NTL_EFF_BB_MUL_CODE2 NTL_ALT1_BB_MUL_CODE2 |
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312 | #define NTL_EFF_SHORT_BB_MUL_CODE1 NTL_ALT1_SHORT_BB_MUL_CODE1 |
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313 | #define NTL_EFF_HALF_BB_MUL_CODE0 NTL_ALT1_HALF_BB_MUL_CODE0 |
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314 | |
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315 | #elif (defined(NTL_GF2X_ALTCODE)) |
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316 | |
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317 | #define NTL_EFF_BB_MUL_CODE0 NTL_ALT_BB_MUL_CODE0 |
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318 | #define NTL_EFF_BB_MUL_CODE1 NTL_ALT_BB_MUL_CODE1 |
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319 | #define NTL_EFF_BB_MUL_CODE2 NTL_ALT_BB_MUL_CODE2 |
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320 | #define NTL_EFF_SHORT_BB_MUL_CODE1 NTL_ALT_SHORT_BB_MUL_CODE1 |
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321 | #define NTL_EFF_HALF_BB_MUL_CODE0 NTL_ALT_HALF_BB_MUL_CODE0 |
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322 | |
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323 | #else |
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324 | |
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325 | #define NTL_EFF_BB_MUL_CODE0 NTL_BB_MUL_CODE0 |
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326 | #define NTL_EFF_BB_MUL_CODE1 NTL_BB_MUL_CODE1 |
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327 | #define NTL_EFF_BB_MUL_CODE2 NTL_BB_MUL_CODE2 |
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328 | #define NTL_EFF_SHORT_BB_MUL_CODE1 NTL_SHORT_BB_MUL_CODE1 |
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329 | #define NTL_EFF_HALF_BB_MUL_CODE0 NTL_HALF_BB_MUL_CODE0 |
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330 | |
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331 | #endif |
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332 | |
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333 | |
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334 | |
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335 | static |
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336 | void mul1(_ntl_ulong *c, _ntl_ulong a, _ntl_ulong b) |
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337 | { |
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338 | |
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339 | NTL_EFF_BB_MUL_CODE0 |
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340 | |
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341 | |
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342 | } |
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343 | |
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344 | |
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345 | #ifdef NTL_GF2X_NOINLINE |
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346 | |
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347 | #define mul1_IL mul1 |
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348 | |
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349 | #else |
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350 | |
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351 | static inline |
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352 | void mul1_inline(_ntl_ulong *c, _ntl_ulong a, _ntl_ulong b) |
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353 | { |
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354 | |
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355 | |
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356 | NTL_EFF_BB_MUL_CODE0 |
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357 | |
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358 | |
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359 | } |
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360 | |
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361 | #define mul1_IL mul1_inline |
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362 | #endif |
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363 | |
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364 | |
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365 | static |
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366 | void Mul1(_ntl_ulong *cp, const _ntl_ulong *bp, long sb, _ntl_ulong a) |
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367 | { |
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368 | |
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369 | |
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370 | NTL_EFF_BB_MUL_CODE1 |
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371 | |
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372 | |
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373 | } |
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374 | |
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375 | static |
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376 | void AddMul1(_ntl_ulong *cp, const _ntl_ulong* bp, long sb, _ntl_ulong a) |
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377 | { |
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378 | |
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379 | |
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380 | NTL_EFF_BB_MUL_CODE2 |
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381 | |
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382 | |
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383 | } |
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384 | |
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385 | |
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386 | static |
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387 | void Mul1_short(_ntl_ulong *cp, const _ntl_ulong *bp, long sb, _ntl_ulong a) |
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388 | { |
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389 | |
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390 | |
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391 | NTL_EFF_SHORT_BB_MUL_CODE1 |
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392 | |
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393 | |
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394 | } |
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395 | |
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396 | |
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397 | |
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398 | |
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399 | |
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400 | static |
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401 | void mul_half(_ntl_ulong *c, _ntl_ulong a, _ntl_ulong b) |
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402 | { |
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403 | |
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404 | |
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405 | NTL_EFF_HALF_BB_MUL_CODE0 |
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406 | |
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407 | |
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408 | } |
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409 | |
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410 | |
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411 | // mul2...mul8 hard-code 2x2...8x8 word multiplies. |
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412 | // I adapted these routines from LiDIA (except mul3, see below). |
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413 | // Inlining these seems to hurt, not help. |
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414 | |
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415 | static |
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416 | void mul2(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
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417 | { |
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418 | _ntl_ulong hs0, hs1; |
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419 | _ntl_ulong hl2[2]; |
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420 | |
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421 | hs0 = a[0] ^ a[1]; |
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422 | hs1 = b[0] ^ b[1]; |
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423 | |
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424 | mul1_IL(c, a[0], b[0]); |
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425 | mul1_IL(c+2, a[1], b[1]); |
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426 | mul1_IL(hl2, hs0, hs1); |
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427 | |
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428 | |
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429 | hl2[0] = hl2[0] ^ c[0] ^ c[2]; |
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430 | hl2[1] = hl2[1] ^ c[1] ^ c[3]; |
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431 | |
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432 | c[1] ^= hl2[0]; |
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433 | c[2] ^= hl2[1]; |
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434 | } |
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435 | |
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436 | |
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437 | /* |
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438 | * This version of mul3 I got from Weimerskirch, Stebila, |
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439 | * and Shantz, "Generic GF(2^m) arithmetic in software |
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440 | * an its application to ECC" (ACISP 2003). |
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441 | */ |
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442 | |
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443 | static |
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444 | void mul3 (_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
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445 | { |
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446 | _ntl_ulong d0[2], d1[2], d2[2], d01[2], d02[2], d12[2]; |
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447 | |
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448 | mul1_IL(d0, a[0], b[0]); |
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449 | mul1_IL(d1, a[1], b[1]); |
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450 | mul1_IL(d2, a[2], b[2]); |
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451 | mul1_IL(d01, a[0]^a[1], b[0]^b[1]); |
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452 | mul1_IL(d02, a[0]^a[2], b[0]^b[2]); |
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453 | mul1_IL(d12, a[1]^a[2], b[1]^b[2]); |
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454 | |
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455 | |
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456 | c[0] = d0[0]; |
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457 | c[1] = d0[1] ^ d01[0] ^ d1[0] ^ d0[0]; |
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458 | c[2] = d01[1] ^ d1[1] ^ d0[1] ^ d02[0] ^ d2[0] ^ d0[0] ^ d1[0]; |
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459 | c[3] = d02[1] ^ d2[1] ^ d0[1] ^ d1[1] ^ d12[0] ^ d1[0] ^ d2[0]; |
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460 | c[4] = d12[1] ^ d1[1] ^ d2[1] ^ d2[0]; |
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461 | c[5] = d2[1]; |
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462 | |
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463 | } |
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464 | |
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465 | static |
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466 | void mul4(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
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467 | { |
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468 | _ntl_ulong hs0[2], hs1[2]; |
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469 | _ntl_ulong hl2[4]; |
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470 | |
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471 | hs0[0] = a[0] ^ a[2]; |
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472 | hs0[1] = a[1] ^ a[3]; |
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473 | hs1[0] = b[0] ^ b[2]; |
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474 | hs1[1] = b[1] ^ b[3]; |
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475 | |
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476 | mul2(c, a, b); |
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477 | mul2(c+4, a+2, b+2); |
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478 | mul2(hl2, hs0, hs1); |
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479 | |
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480 | hl2[0] = hl2[0] ^ c[0] ^ c[4]; |
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481 | hl2[1] = hl2[1] ^ c[1] ^ c[5]; |
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482 | hl2[2] = hl2[2] ^ c[2] ^ c[6]; |
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483 | hl2[3] = hl2[3] ^ c[3] ^ c[7]; |
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484 | |
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485 | c[2] ^= hl2[0]; |
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486 | c[3] ^= hl2[1]; |
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487 | c[4] ^= hl2[2]; |
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488 | c[5] ^= hl2[3]; |
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489 | } |
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490 | |
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491 | static |
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492 | void mul5 (_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
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493 | { |
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494 | _ntl_ulong hs0[3], hs1[3]; |
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495 | _ntl_ulong hl2[6]; |
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496 | |
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497 | hs0[0] = a[0] ^ a[3]; |
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498 | hs0[1] = a[1] ^ a[4]; |
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499 | hs0[2] = a[2]; |
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500 | hs1[0] = b[0] ^ b[3]; |
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501 | hs1[1] = b[1] ^ b[4]; |
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502 | hs1[2] = b[2]; |
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503 | |
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504 | mul3(c, a, b); |
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505 | mul3(hl2, hs0, hs1); |
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506 | mul2(c+6, a+3, b+3); |
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507 | |
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508 | hl2[0] = hl2[0] ^ c[0] ^ c[6]; |
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509 | hl2[1] = hl2[1] ^ c[1] ^ c[7]; |
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510 | hl2[2] = hl2[2] ^ c[2] ^ c[8]; |
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511 | hl2[3] = hl2[3] ^ c[3] ^ c[9]; |
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512 | hl2[4] = hl2[4] ^ c[4]; |
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513 | hl2[5] = hl2[5] ^ c[5]; |
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514 | |
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515 | |
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516 | c[3] ^= hl2[0]; |
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517 | c[4] ^= hl2[1]; |
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518 | c[5] ^= hl2[2]; |
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519 | c[6] ^= hl2[3]; |
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520 | c[7] ^= hl2[4]; |
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521 | c[8] ^= hl2[5]; |
---|
522 | } |
---|
523 | |
---|
524 | static |
---|
525 | void mul6(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
---|
526 | { |
---|
527 | _ntl_ulong hs0[3], hs1[3]; |
---|
528 | _ntl_ulong hl2[6]; |
---|
529 | |
---|
530 | hs0[0] = a[0] ^ a[3]; |
---|
531 | hs0[1] = a[1] ^ a[4]; |
---|
532 | hs0[2] = a[2] ^ a[5]; |
---|
533 | hs1[0] = b[0] ^ b[3]; |
---|
534 | hs1[1] = b[1] ^ b[4]; |
---|
535 | hs1[2] = b[2] ^ b[5]; |
---|
536 | |
---|
537 | mul3(c, a, b); |
---|
538 | mul3(c+6, a+3, b+3); |
---|
539 | mul3(hl2, hs0, hs1); |
---|
540 | |
---|
541 | hl2[0] = hl2[0] ^ c[0] ^ c[6]; |
---|
542 | hl2[1] = hl2[1] ^ c[1] ^ c[7]; |
---|
543 | hl2[2] = hl2[2] ^ c[2] ^ c[8]; |
---|
544 | hl2[3] = hl2[3] ^ c[3] ^ c[9]; |
---|
545 | hl2[4] = hl2[4] ^ c[4] ^ c[10]; |
---|
546 | hl2[5] = hl2[5] ^ c[5] ^ c[11]; |
---|
547 | |
---|
548 | c[3] ^= hl2[0]; |
---|
549 | c[4] ^= hl2[1]; |
---|
550 | c[5] ^= hl2[2]; |
---|
551 | c[6] ^= hl2[3]; |
---|
552 | c[7] ^= hl2[4]; |
---|
553 | c[8] ^= hl2[5]; |
---|
554 | } |
---|
555 | |
---|
556 | static |
---|
557 | void mul7(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
---|
558 | { |
---|
559 | _ntl_ulong hs0[4], hs1[4]; |
---|
560 | _ntl_ulong hl2[8]; |
---|
561 | |
---|
562 | hs0[0] = a[0] ^ a[4]; |
---|
563 | hs0[1] = a[1] ^ a[5]; |
---|
564 | hs0[2] = a[2] ^ a[6]; |
---|
565 | hs0[3] = a[3]; |
---|
566 | hs1[0] = b[0] ^ b[4]; |
---|
567 | hs1[1] = b[1] ^ b[5]; |
---|
568 | hs1[2] = b[2] ^ b[6]; |
---|
569 | hs1[3] = b[3]; |
---|
570 | |
---|
571 | mul4(c, a, b); |
---|
572 | mul4(hl2, hs0, hs1); |
---|
573 | mul3(c+8, a+4, b+4); |
---|
574 | |
---|
575 | hl2[0] = hl2[0] ^ c[0] ^ c[8]; |
---|
576 | hl2[1] = hl2[1] ^ c[1] ^ c[9]; |
---|
577 | hl2[2] = hl2[2] ^ c[2] ^ c[10]; |
---|
578 | hl2[3] = hl2[3] ^ c[3] ^ c[11]; |
---|
579 | hl2[4] = hl2[4] ^ c[4] ^ c[12]; |
---|
580 | hl2[5] = hl2[5] ^ c[5] ^ c[13]; |
---|
581 | hl2[6] = hl2[6] ^ c[6]; |
---|
582 | hl2[7] = hl2[7] ^ c[7]; |
---|
583 | |
---|
584 | c[4] ^= hl2[0]; |
---|
585 | c[5] ^= hl2[1]; |
---|
586 | c[6] ^= hl2[2]; |
---|
587 | c[7] ^= hl2[3]; |
---|
588 | c[8] ^= hl2[4]; |
---|
589 | c[9] ^= hl2[5]; |
---|
590 | c[10] ^= hl2[6]; |
---|
591 | c[11] ^= hl2[7]; |
---|
592 | } |
---|
593 | |
---|
594 | static |
---|
595 | void mul8(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b) |
---|
596 | { |
---|
597 | _ntl_ulong hs0[4], hs1[4]; |
---|
598 | _ntl_ulong hl2[8]; |
---|
599 | |
---|
600 | hs0[0] = a[0] ^ a[4]; |
---|
601 | hs0[1] = a[1] ^ a[5]; |
---|
602 | hs0[2] = a[2] ^ a[6]; |
---|
603 | hs0[3] = a[3] ^ a[7]; |
---|
604 | hs1[0] = b[0] ^ b[4]; |
---|
605 | hs1[1] = b[1] ^ b[5]; |
---|
606 | hs1[2] = b[2] ^ b[6]; |
---|
607 | hs1[3] = b[3] ^ b[7]; |
---|
608 | |
---|
609 | mul4(c, a, b); |
---|
610 | mul4(c+8, a+4, b+4); |
---|
611 | mul4(hl2, hs0, hs1); |
---|
612 | |
---|
613 | hl2[0] = hl2[0] ^ c[0] ^ c[8]; |
---|
614 | hl2[1] = hl2[1] ^ c[1] ^ c[9]; |
---|
615 | hl2[2] = hl2[2] ^ c[2] ^ c[10]; |
---|
616 | hl2[3] = hl2[3] ^ c[3] ^ c[11]; |
---|
617 | hl2[4] = hl2[4] ^ c[4] ^ c[12]; |
---|
618 | hl2[5] = hl2[5] ^ c[5] ^ c[13]; |
---|
619 | hl2[6] = hl2[6] ^ c[6] ^ c[14]; |
---|
620 | hl2[7] = hl2[7] ^ c[7] ^ c[15]; |
---|
621 | |
---|
622 | c[4] ^= hl2[0]; |
---|
623 | c[5] ^= hl2[1]; |
---|
624 | c[6] ^= hl2[2]; |
---|
625 | c[7] ^= hl2[3]; |
---|
626 | c[8] ^= hl2[4]; |
---|
627 | c[9] ^= hl2[5]; |
---|
628 | c[10] ^= hl2[6]; |
---|
629 | c[11] ^= hl2[7]; |
---|
630 | } |
---|
631 | |
---|
632 | static |
---|
633 | void KarMul(_ntl_ulong *c, const _ntl_ulong *a, const _ntl_ulong *b, |
---|
634 | long len, _ntl_ulong *stk) |
---|
635 | { |
---|
636 | if (len <= 8) { |
---|
637 | switch (len) { |
---|
638 | case 1: mul1(c, a[0], b[0]); break; |
---|
639 | case 2: mul2(c, a, b); break; |
---|
640 | case 3: mul3(c, a, b); break; |
---|
641 | case 4: mul4(c, a, b); break; |
---|
642 | case 5: mul5(c, a, b); break; |
---|
643 | case 6: mul6(c, a, b); break; |
---|
644 | case 7: mul7(c, a, b); break; |
---|
645 | case 8: mul8(c, a, b); break; |
---|
646 | } |
---|
647 | |
---|
648 | return; |
---|
649 | } |
---|
650 | |
---|
651 | long ll, lh, i, ll2, lh2; |
---|
652 | const _ntl_ulong *a0, *a1, *b0, *b1; |
---|
653 | _ntl_ulong *a01, *b01, *h; |
---|
654 | |
---|
655 | |
---|
656 | lh = len >> 1; |
---|
657 | ll = (len+1) >> 1; |
---|
658 | |
---|
659 | ll2 = ll << 1; |
---|
660 | lh2 = lh << 1; |
---|
661 | |
---|
662 | a01 = stk; stk += ll+1; |
---|
663 | b01 = stk; stk += ll+1; |
---|
664 | h = stk; stk += ll2+1; |
---|
665 | |
---|
666 | a0 = a; |
---|
667 | a1 = a+ll; |
---|
668 | b0 = b; |
---|
669 | b1 = b+ll; |
---|
670 | |
---|
671 | KarMul(c, a0, b0, ll, stk); |
---|
672 | KarMul(c+ll2, a1, b1, lh, stk); |
---|
673 | |
---|
674 | for (i = 0; i < lh; i++) { |
---|
675 | a01[i] = a[i] ^ a[i+ll]; |
---|
676 | b01[i] = b[i] ^ b[i+ll]; |
---|
677 | } |
---|
678 | |
---|
679 | if (lh < ll) { |
---|
680 | a01[lh] = a[lh]; |
---|
681 | b01[lh] = b[lh]; |
---|
682 | } |
---|
683 | |
---|
684 | KarMul(h, a01, b01, ll, stk); |
---|
685 | |
---|
686 | for (i = 0; i < ll2; i++) |
---|
687 | h[i] ^= c[i]; |
---|
688 | |
---|
689 | for (i = 0; i < lh2; i++) |
---|
690 | h[i] ^= c[i+ll2]; |
---|
691 | |
---|
692 | for (i = 0; i < ll2; i++) |
---|
693 | c[i+ll] ^= h[i]; |
---|
694 | } |
---|
695 | |
---|
696 | |
---|
697 | |
---|
698 | void mul(GF2X& c, const GF2X& a, const GF2X& b) |
---|
699 | { |
---|
700 | long sa = a.xrep.length(); |
---|
701 | long sb = b.xrep.length(); |
---|
702 | |
---|
703 | if (sa <= 0 || sb <= 0) { |
---|
704 | clear(c); |
---|
705 | return; |
---|
706 | } |
---|
707 | |
---|
708 | _ntl_ulong a0 = a.xrep[0]; |
---|
709 | _ntl_ulong b0 = b.xrep[0]; |
---|
710 | |
---|
711 | if (sb == 1 && b0 == 1) { |
---|
712 | c = a; |
---|
713 | return; |
---|
714 | } |
---|
715 | |
---|
716 | if (sa == 1 && a0 == 1) { |
---|
717 | c = b; |
---|
718 | return; |
---|
719 | } |
---|
720 | |
---|
721 | if (&a == &b) { |
---|
722 | sqr(c, a); |
---|
723 | return; |
---|
724 | } |
---|
725 | |
---|
726 | if (sa == sb && sa <= 8) { |
---|
727 | // we treat these cases specially for efficiency reasons |
---|
728 | |
---|
729 | switch (sa) { |
---|
730 | case 1: { |
---|
731 | _ntl_ulong v[2]; |
---|
732 | if (!(a0 >> NTL_BITS_PER_LONG/2)) |
---|
733 | mul_half(v, b0, a0); |
---|
734 | else if (!(b0 >> NTL_BITS_PER_LONG/2)) |
---|
735 | mul_half(v, a0, b0); |
---|
736 | else |
---|
737 | mul1(v, a0, b0); |
---|
738 | |
---|
739 | if (v[1]) { |
---|
740 | c.xrep.SetLength(2); |
---|
741 | _ntl_ulong *cp = &c.xrep[0]; |
---|
742 | cp[0] = v[0]; |
---|
743 | cp[1] = v[1]; |
---|
744 | } |
---|
745 | else { |
---|
746 | c.xrep.SetLength(1); |
---|
747 | _ntl_ulong *cp = &c.xrep[0]; |
---|
748 | cp[0] = v[0]; |
---|
749 | } |
---|
750 | } |
---|
751 | return; |
---|
752 | |
---|
753 | case 2: { |
---|
754 | _ntl_ulong v[4]; |
---|
755 | mul2(v, &a.xrep[0], &b.xrep[0]); |
---|
756 | if (v[3]) { |
---|
757 | c.xrep.SetLength(4); |
---|
758 | _ntl_ulong *cp = &c.xrep[0]; |
---|
759 | cp[0] = v[0]; |
---|
760 | cp[1] = v[1]; |
---|
761 | cp[2] = v[2]; |
---|
762 | cp[3] = v[3]; |
---|
763 | } |
---|
764 | else { |
---|
765 | c.xrep.SetLength(3); |
---|
766 | _ntl_ulong *cp = &c.xrep[0]; |
---|
767 | cp[0] = v[0]; |
---|
768 | cp[1] = v[1]; |
---|
769 | cp[2] = v[2]; |
---|
770 | } |
---|
771 | } |
---|
772 | return; |
---|
773 | |
---|
774 | case 3: { |
---|
775 | _ntl_ulong v[6]; |
---|
776 | mul3(v, &a.xrep[0], &b.xrep[0]); |
---|
777 | if (v[5]) { |
---|
778 | c.xrep.SetLength(6); |
---|
779 | _ntl_ulong *cp = &c.xrep[0]; |
---|
780 | cp[0] = v[0]; |
---|
781 | cp[1] = v[1]; |
---|
782 | cp[2] = v[2]; |
---|
783 | cp[3] = v[3]; |
---|
784 | cp[4] = v[4]; |
---|
785 | cp[5] = v[5]; |
---|
786 | } |
---|
787 | else { |
---|
788 | c.xrep.SetLength(5); |
---|
789 | _ntl_ulong *cp = &c.xrep[0]; |
---|
790 | cp[0] = v[0]; |
---|
791 | cp[1] = v[1]; |
---|
792 | cp[2] = v[2]; |
---|
793 | cp[3] = v[3]; |
---|
794 | cp[4] = v[4]; |
---|
795 | } |
---|
796 | } |
---|
797 | return; |
---|
798 | |
---|
799 | case 4: { |
---|
800 | _ntl_ulong v[8]; |
---|
801 | mul4(v, &a.xrep[0], &b.xrep[0]); |
---|
802 | if (v[7]) { |
---|
803 | c.xrep.SetLength(8); |
---|
804 | _ntl_ulong *cp = &c.xrep[0]; |
---|
805 | cp[0] = v[0]; |
---|
806 | cp[1] = v[1]; |
---|
807 | cp[2] = v[2]; |
---|
808 | cp[3] = v[3]; |
---|
809 | cp[4] = v[4]; |
---|
810 | cp[5] = v[5]; |
---|
811 | cp[6] = v[6]; |
---|
812 | cp[7] = v[7]; |
---|
813 | } |
---|
814 | else { |
---|
815 | c.xrep.SetLength(7); |
---|
816 | _ntl_ulong *cp = &c.xrep[0]; |
---|
817 | cp[0] = v[0]; |
---|
818 | cp[1] = v[1]; |
---|
819 | cp[2] = v[2]; |
---|
820 | cp[3] = v[3]; |
---|
821 | cp[4] = v[4]; |
---|
822 | cp[5] = v[5]; |
---|
823 | cp[6] = v[6]; |
---|
824 | } |
---|
825 | } |
---|
826 | return; |
---|
827 | |
---|
828 | case 5: { |
---|
829 | _ntl_ulong v[10]; |
---|
830 | mul5(v, &a.xrep[0], &b.xrep[0]); |
---|
831 | if (v[9]) { |
---|
832 | c.xrep.SetLength(10); |
---|
833 | _ntl_ulong *cp = &c.xrep[0]; |
---|
834 | cp[0] = v[0]; |
---|
835 | cp[1] = v[1]; |
---|
836 | cp[2] = v[2]; |
---|
837 | cp[3] = v[3]; |
---|
838 | cp[4] = v[4]; |
---|
839 | cp[5] = v[5]; |
---|
840 | cp[6] = v[6]; |
---|
841 | cp[7] = v[7]; |
---|
842 | cp[8] = v[8]; |
---|
843 | cp[9] = v[9]; |
---|
844 | } |
---|
845 | else { |
---|
846 | c.xrep.SetLength(9); |
---|
847 | _ntl_ulong *cp = &c.xrep[0]; |
---|
848 | cp[0] = v[0]; |
---|
849 | cp[1] = v[1]; |
---|
850 | cp[2] = v[2]; |
---|
851 | cp[3] = v[3]; |
---|
852 | cp[4] = v[4]; |
---|
853 | cp[5] = v[5]; |
---|
854 | cp[6] = v[6]; |
---|
855 | cp[7] = v[7]; |
---|
856 | cp[8] = v[8]; |
---|
857 | } |
---|
858 | } |
---|
859 | return; |
---|
860 | |
---|
861 | case 6: { |
---|
862 | _ntl_ulong v[12]; |
---|
863 | mul6(v, &a.xrep[0], &b.xrep[0]); |
---|
864 | if (v[11]) { |
---|
865 | c.xrep.SetLength(12); |
---|
866 | _ntl_ulong *cp = &c.xrep[0]; |
---|
867 | cp[0] = v[0]; |
---|
868 | cp[1] = v[1]; |
---|
869 | cp[2] = v[2]; |
---|
870 | cp[3] = v[3]; |
---|
871 | cp[4] = v[4]; |
---|
872 | cp[5] = v[5]; |
---|
873 | cp[6] = v[6]; |
---|
874 | cp[7] = v[7]; |
---|
875 | cp[8] = v[8]; |
---|
876 | cp[9] = v[9]; |
---|
877 | cp[10] = v[10]; |
---|
878 | cp[11] = v[11]; |
---|
879 | } |
---|
880 | else { |
---|
881 | c.xrep.SetLength(11); |
---|
882 | _ntl_ulong *cp = &c.xrep[0]; |
---|
883 | cp[0] = v[0]; |
---|
884 | cp[1] = v[1]; |
---|
885 | cp[2] = v[2]; |
---|
886 | cp[3] = v[3]; |
---|
887 | cp[4] = v[4]; |
---|
888 | cp[5] = v[5]; |
---|
889 | cp[6] = v[6]; |
---|
890 | cp[7] = v[7]; |
---|
891 | cp[8] = v[8]; |
---|
892 | cp[9] = v[9]; |
---|
893 | cp[10] = v[10]; |
---|
894 | } |
---|
895 | } |
---|
896 | return; |
---|
897 | |
---|
898 | case 7: { |
---|
899 | _ntl_ulong v[14]; |
---|
900 | mul7(v, &a.xrep[0], &b.xrep[0]); |
---|
901 | if (v[13]) { |
---|
902 | c.xrep.SetLength(14); |
---|
903 | _ntl_ulong *cp = &c.xrep[0]; |
---|
904 | cp[0] = v[0]; |
---|
905 | cp[1] = v[1]; |
---|
906 | cp[2] = v[2]; |
---|
907 | cp[3] = v[3]; |
---|
908 | cp[4] = v[4]; |
---|
909 | cp[5] = v[5]; |
---|
910 | cp[6] = v[6]; |
---|
911 | cp[7] = v[7]; |
---|
912 | cp[8] = v[8]; |
---|
913 | cp[9] = v[9]; |
---|
914 | cp[10] = v[10]; |
---|
915 | cp[11] = v[11]; |
---|
916 | cp[12] = v[12]; |
---|
917 | cp[13] = v[13]; |
---|
918 | } |
---|
919 | else { |
---|
920 | c.xrep.SetLength(13); |
---|
921 | _ntl_ulong *cp = &c.xrep[0]; |
---|
922 | cp[0] = v[0]; |
---|
923 | cp[1] = v[1]; |
---|
924 | cp[2] = v[2]; |
---|
925 | cp[3] = v[3]; |
---|
926 | cp[4] = v[4]; |
---|
927 | cp[5] = v[5]; |
---|
928 | cp[6] = v[6]; |
---|
929 | cp[7] = v[7]; |
---|
930 | cp[8] = v[8]; |
---|
931 | cp[9] = v[9]; |
---|
932 | cp[10] = v[10]; |
---|
933 | cp[11] = v[11]; |
---|
934 | cp[12] = v[12]; |
---|
935 | } |
---|
936 | } |
---|
937 | return; |
---|
938 | |
---|
939 | case 8: { |
---|
940 | _ntl_ulong v[16]; |
---|
941 | mul8(v, &a.xrep[0], &b.xrep[0]); |
---|
942 | if (v[15]) { |
---|
943 | c.xrep.SetLength(16); |
---|
944 | _ntl_ulong *cp = &c.xrep[0]; |
---|
945 | cp[0] = v[0]; |
---|
946 | cp[1] = v[1]; |
---|
947 | cp[2] = v[2]; |
---|
948 | cp[3] = v[3]; |
---|
949 | cp[4] = v[4]; |
---|
950 | cp[5] = v[5]; |
---|
951 | cp[6] = v[6]; |
---|
952 | cp[7] = v[7]; |
---|
953 | cp[8] = v[8]; |
---|
954 | cp[9] = v[9]; |
---|
955 | cp[10] = v[10]; |
---|
956 | cp[11] = v[11]; |
---|
957 | cp[12] = v[12]; |
---|
958 | cp[13] = v[13]; |
---|
959 | cp[14] = v[14]; |
---|
960 | cp[15] = v[15]; |
---|
961 | } |
---|
962 | else { |
---|
963 | c.xrep.SetLength(15); |
---|
964 | _ntl_ulong *cp = &c.xrep[0]; |
---|
965 | cp[0] = v[0]; |
---|
966 | cp[1] = v[1]; |
---|
967 | cp[2] = v[2]; |
---|
968 | cp[3] = v[3]; |
---|
969 | cp[4] = v[4]; |
---|
970 | cp[5] = v[5]; |
---|
971 | cp[6] = v[6]; |
---|
972 | cp[7] = v[7]; |
---|
973 | cp[8] = v[8]; |
---|
974 | cp[9] = v[9]; |
---|
975 | cp[10] = v[10]; |
---|
976 | cp[11] = v[11]; |
---|
977 | cp[12] = v[12]; |
---|
978 | cp[13] = v[13]; |
---|
979 | cp[14] = v[14]; |
---|
980 | } |
---|
981 | } |
---|
982 | return; |
---|
983 | |
---|
984 | } |
---|
985 | } |
---|
986 | |
---|
987 | // another special case: one of the two inputs |
---|
988 | // has length 1 (or less). |
---|
989 | |
---|
990 | if (sa == 1) { |
---|
991 | c.xrep.SetLength(sb + 1); |
---|
992 | _ntl_ulong *cp = c.xrep.elts(); |
---|
993 | const _ntl_ulong *bp = b.xrep.elts(); |
---|
994 | |
---|
995 | if (a0 >> (NTL_BITS_PER_LONG-NTL_BB_MUL1_BITS+1)) |
---|
996 | Mul1(cp, bp, sb, a0); |
---|
997 | else |
---|
998 | Mul1_short(cp, bp, sb, a0); |
---|
999 | |
---|
1000 | |
---|
1001 | c.normalize(); |
---|
1002 | return; |
---|
1003 | } |
---|
1004 | |
---|
1005 | if (sb == 1) { |
---|
1006 | c.xrep.SetLength(sa + 1); |
---|
1007 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1008 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1009 | |
---|
1010 | |
---|
1011 | if (b0 >> (NTL_BITS_PER_LONG-NTL_BB_MUL1_BITS+1)) |
---|
1012 | Mul1(cp, ap, sa, b0); |
---|
1013 | else |
---|
1014 | Mul1_short(cp, ap, sa, b0); |
---|
1015 | |
---|
1016 | c.normalize(); |
---|
1017 | return; |
---|
1018 | } |
---|
1019 | |
---|
1020 | // finally: the general case |
---|
1021 | |
---|
1022 | |
---|
1023 | static WordVector mem; |
---|
1024 | static WordVector stk; |
---|
1025 | static WordVector vec; |
---|
1026 | |
---|
1027 | const _ntl_ulong *ap, *bp; |
---|
1028 | _ntl_ulong *cp; |
---|
1029 | |
---|
1030 | |
---|
1031 | long sc = sa + sb; |
---|
1032 | long in_mem = 0; |
---|
1033 | |
---|
1034 | if (&a == &c || &b == &c) { |
---|
1035 | mem.SetLength(sc); |
---|
1036 | cp = mem.elts(); |
---|
1037 | in_mem = 1; |
---|
1038 | } |
---|
1039 | else { |
---|
1040 | c.xrep.SetLength(sc); |
---|
1041 | cp = c.xrep.elts(); |
---|
1042 | } |
---|
1043 | |
---|
1044 | |
---|
1045 | long n, hn, sp; |
---|
1046 | |
---|
1047 | n = min(sa, sb); |
---|
1048 | sp = 0; |
---|
1049 | while (n > 8) { |
---|
1050 | hn = (n+1) >> 1; |
---|
1051 | sp += (hn << 2) + 3; |
---|
1052 | n = hn; |
---|
1053 | } |
---|
1054 | |
---|
1055 | stk.SetLength(sp); |
---|
1056 | _ntl_ulong *stk_p = stk.elts(); |
---|
1057 | |
---|
1058 | if (sa > sb) { |
---|
1059 | { long t; t = sa; sa = sb; sb = t; } |
---|
1060 | ap = b.xrep.elts(); |
---|
1061 | bp = a.xrep.elts(); |
---|
1062 | } |
---|
1063 | else { |
---|
1064 | ap = a.xrep.elts(); |
---|
1065 | bp = b.xrep.elts(); |
---|
1066 | } |
---|
1067 | |
---|
1068 | |
---|
1069 | vec.SetLength(2*sa); |
---|
1070 | |
---|
1071 | _ntl_ulong *v = vec.elts(); |
---|
1072 | |
---|
1073 | long i, j; |
---|
1074 | |
---|
1075 | for (i = 0; i < sc; i++) |
---|
1076 | cp[i] = 0; |
---|
1077 | |
---|
1078 | do { |
---|
1079 | if (sa == 0) break; |
---|
1080 | |
---|
1081 | if (sa == 1) { |
---|
1082 | AddMul1(cp, bp, sb, ap[0]); |
---|
1083 | |
---|
1084 | break; |
---|
1085 | } |
---|
1086 | |
---|
1087 | // general case |
---|
1088 | |
---|
1089 | for (i = 0; i+sa <= sb; i += sa) { |
---|
1090 | KarMul(v, ap, bp + i, sa, stk_p); |
---|
1091 | for (j = 0; j < 2*sa; j++) |
---|
1092 | cp[i+j] ^= v[j]; |
---|
1093 | } |
---|
1094 | |
---|
1095 | { const _ntl_ulong *t; t = ap; ap = bp + i; bp = t; } |
---|
1096 | { long t; t = sa; sa = sb - i; sb = t; } |
---|
1097 | cp = cp + i; |
---|
1098 | } while (1); |
---|
1099 | |
---|
1100 | if (in_mem) |
---|
1101 | c.xrep = mem; |
---|
1102 | |
---|
1103 | c.normalize(); |
---|
1104 | } |
---|
1105 | |
---|
1106 | |
---|
1107 | |
---|
1108 | |
---|
1109 | void mul(GF2X& c, const GF2X& a, long b) |
---|
1110 | { |
---|
1111 | if (b & 1) |
---|
1112 | c = a; |
---|
1113 | else |
---|
1114 | clear(c); |
---|
1115 | } |
---|
1116 | |
---|
1117 | void mul(GF2X& c, const GF2X& a, GF2 b) |
---|
1118 | { |
---|
1119 | if (b == 1) |
---|
1120 | c = a; |
---|
1121 | else |
---|
1122 | clear(c); |
---|
1123 | } |
---|
1124 | |
---|
1125 | |
---|
1126 | void trunc(GF2X& x, const GF2X& a, long m) |
---|
1127 | { |
---|
1128 | if (m < 0) Error("trunc: bad args"); |
---|
1129 | |
---|
1130 | long n = a.xrep.length(); |
---|
1131 | if (n == 0 || m == 0) { |
---|
1132 | clear(x); |
---|
1133 | return; |
---|
1134 | } |
---|
1135 | |
---|
1136 | if (&x == &a) { |
---|
1137 | if (n*NTL_BITS_PER_LONG > m) { |
---|
1138 | long wm = (m-1)/NTL_BITS_PER_LONG; |
---|
1139 | long bm = m - NTL_BITS_PER_LONG*wm; |
---|
1140 | _ntl_ulong msk; |
---|
1141 | if (bm == NTL_BITS_PER_LONG) |
---|
1142 | msk = ~(0UL); |
---|
1143 | else |
---|
1144 | msk = ((1UL << bm) - 1UL); |
---|
1145 | x.xrep[wm] &= msk; |
---|
1146 | x.xrep.QuickSetLength(wm+1); |
---|
1147 | x.normalize(); |
---|
1148 | } |
---|
1149 | } |
---|
1150 | else if (n*NTL_BITS_PER_LONG <= m) |
---|
1151 | x = a; |
---|
1152 | else { |
---|
1153 | long wm = (m-1)/NTL_BITS_PER_LONG; |
---|
1154 | long bm = m - NTL_BITS_PER_LONG*wm; |
---|
1155 | x.xrep.SetLength(wm+1); |
---|
1156 | _ntl_ulong *xp = &x.xrep[0]; |
---|
1157 | const _ntl_ulong *ap = &a.xrep[0]; |
---|
1158 | long i; |
---|
1159 | for (i = 0; i < wm; i++) |
---|
1160 | xp[i] = ap[i]; |
---|
1161 | _ntl_ulong msk; |
---|
1162 | if (bm == NTL_BITS_PER_LONG) |
---|
1163 | msk = ~(0UL); |
---|
1164 | else |
---|
1165 | msk = ((1UL << bm) - 1UL); |
---|
1166 | xp[wm] = ap[wm] & msk; |
---|
1167 | x.normalize(); |
---|
1168 | } |
---|
1169 | } |
---|
1170 | |
---|
1171 | |
---|
1172 | /****** implementation of vec_GF2X ******/ |
---|
1173 | |
---|
1174 | |
---|
1175 | NTL_vector_impl(GF2X,vec_GF2X) |
---|
1176 | |
---|
1177 | NTL_eq_vector_impl(GF2X,vec_GF2X) |
---|
1178 | |
---|
1179 | |
---|
1180 | |
---|
1181 | void MulByX(GF2X& x, const GF2X& a) |
---|
1182 | { |
---|
1183 | long n = a.xrep.length(); |
---|
1184 | if (n == 0) { |
---|
1185 | clear(x); |
---|
1186 | return; |
---|
1187 | } |
---|
1188 | |
---|
1189 | if (a.xrep[n-1] & (1UL << (NTL_BITS_PER_LONG-1))) { |
---|
1190 | x.xrep.SetLength(n+1); |
---|
1191 | x.xrep[n] = 1; |
---|
1192 | } |
---|
1193 | else if (&x != &a) |
---|
1194 | x.xrep.SetLength(n); |
---|
1195 | |
---|
1196 | _ntl_ulong *xp = &x.xrep[0]; |
---|
1197 | const _ntl_ulong *ap = &a.xrep[0]; |
---|
1198 | |
---|
1199 | long i; |
---|
1200 | for (i = n-1; i > 0; i--) |
---|
1201 | xp[i] = (ap[i] << 1) | (ap[i-1] >> (NTL_BITS_PER_LONG-1)); |
---|
1202 | |
---|
1203 | xp[0] = ap[0] << 1; |
---|
1204 | |
---|
1205 | // no need to normalize |
---|
1206 | } |
---|
1207 | |
---|
1208 | |
---|
1209 | |
---|
1210 | static _ntl_ulong sqrtab[256] = { |
---|
1211 | |
---|
1212 | 0UL, 1UL, 4UL, 5UL, 16UL, 17UL, 20UL, 21UL, 64UL, |
---|
1213 | 65UL, 68UL, 69UL, 80UL, 81UL, 84UL, 85UL, 256UL, |
---|
1214 | 257UL, 260UL, 261UL, 272UL, 273UL, 276UL, 277UL, 320UL, |
---|
1215 | 321UL, 324UL, 325UL, 336UL, 337UL, 340UL, 341UL, 1024UL, |
---|
1216 | 1025UL, 1028UL, 1029UL, 1040UL, 1041UL, 1044UL, 1045UL, 1088UL, |
---|
1217 | 1089UL, 1092UL, 1093UL, 1104UL, 1105UL, 1108UL, 1109UL, 1280UL, |
---|
1218 | 1281UL, 1284UL, 1285UL, 1296UL, 1297UL, 1300UL, 1301UL, 1344UL, |
---|
1219 | 1345UL, 1348UL, 1349UL, 1360UL, 1361UL, 1364UL, 1365UL, 4096UL, |
---|
1220 | 4097UL, 4100UL, 4101UL, 4112UL, 4113UL, 4116UL, 4117UL, 4160UL, |
---|
1221 | 4161UL, 4164UL, 4165UL, 4176UL, 4177UL, 4180UL, 4181UL, 4352UL, |
---|
1222 | 4353UL, 4356UL, 4357UL, 4368UL, 4369UL, 4372UL, 4373UL, 4416UL, |
---|
1223 | 4417UL, 4420UL, 4421UL, 4432UL, 4433UL, 4436UL, 4437UL, 5120UL, |
---|
1224 | 5121UL, 5124UL, 5125UL, 5136UL, 5137UL, 5140UL, 5141UL, 5184UL, |
---|
1225 | 5185UL, 5188UL, 5189UL, 5200UL, 5201UL, 5204UL, 5205UL, 5376UL, |
---|
1226 | 5377UL, 5380UL, 5381UL, 5392UL, 5393UL, 5396UL, 5397UL, 5440UL, |
---|
1227 | 5441UL, 5444UL, 5445UL, 5456UL, 5457UL, 5460UL, 5461UL, 16384UL, |
---|
1228 | 16385UL, 16388UL, 16389UL, 16400UL, 16401UL, 16404UL, 16405UL, 16448UL, |
---|
1229 | 16449UL, 16452UL, 16453UL, 16464UL, 16465UL, 16468UL, 16469UL, 16640UL, |
---|
1230 | 16641UL, 16644UL, 16645UL, 16656UL, 16657UL, 16660UL, 16661UL, 16704UL, |
---|
1231 | 16705UL, 16708UL, 16709UL, 16720UL, 16721UL, 16724UL, 16725UL, 17408UL, |
---|
1232 | 17409UL, 17412UL, 17413UL, 17424UL, 17425UL, 17428UL, 17429UL, 17472UL, |
---|
1233 | 17473UL, 17476UL, 17477UL, 17488UL, 17489UL, 17492UL, 17493UL, 17664UL, |
---|
1234 | 17665UL, 17668UL, 17669UL, 17680UL, 17681UL, 17684UL, 17685UL, 17728UL, |
---|
1235 | 17729UL, 17732UL, 17733UL, 17744UL, 17745UL, 17748UL, 17749UL, 20480UL, |
---|
1236 | 20481UL, 20484UL, 20485UL, 20496UL, 20497UL, 20500UL, 20501UL, 20544UL, |
---|
1237 | 20545UL, 20548UL, 20549UL, 20560UL, 20561UL, 20564UL, 20565UL, 20736UL, |
---|
1238 | 20737UL, 20740UL, 20741UL, 20752UL, 20753UL, 20756UL, 20757UL, 20800UL, |
---|
1239 | 20801UL, 20804UL, 20805UL, 20816UL, 20817UL, 20820UL, 20821UL, 21504UL, |
---|
1240 | 21505UL, 21508UL, 21509UL, 21520UL, 21521UL, 21524UL, 21525UL, 21568UL, |
---|
1241 | 21569UL, 21572UL, 21573UL, 21584UL, 21585UL, 21588UL, 21589UL, 21760UL, |
---|
1242 | 21761UL, 21764UL, 21765UL, 21776UL, 21777UL, 21780UL, 21781UL, 21824UL, |
---|
1243 | 21825UL, 21828UL, 21829UL, 21840UL, 21841UL, 21844UL, 21845UL }; |
---|
1244 | |
---|
1245 | |
---|
1246 | |
---|
1247 | |
---|
1248 | static inline |
---|
1249 | void sqr1(_ntl_ulong *c, _ntl_ulong a) |
---|
1250 | { |
---|
1251 | _ntl_ulong hi, lo; |
---|
1252 | |
---|
1253 | NTL_BB_SQR_CODE |
---|
1254 | |
---|
1255 | c[0] = lo; |
---|
1256 | c[1] = hi; |
---|
1257 | } |
---|
1258 | |
---|
1259 | |
---|
1260 | |
---|
1261 | |
---|
1262 | void sqr(GF2X& c, const GF2X& a) |
---|
1263 | { |
---|
1264 | long sa = a.xrep.length(); |
---|
1265 | if (sa <= 0) { |
---|
1266 | clear(c); |
---|
1267 | return; |
---|
1268 | } |
---|
1269 | |
---|
1270 | c.xrep.SetLength(sa << 1); |
---|
1271 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1272 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1273 | long i; |
---|
1274 | |
---|
1275 | for (i = sa-1; i >= 0; i--) |
---|
1276 | sqr1(cp + (i << 1), ap[i]); |
---|
1277 | |
---|
1278 | c.normalize(); |
---|
1279 | return; |
---|
1280 | } |
---|
1281 | |
---|
1282 | |
---|
1283 | |
---|
1284 | void LeftShift(GF2X& c, const GF2X& a, long n) |
---|
1285 | { |
---|
1286 | if (IsZero(a)) { |
---|
1287 | clear(c); |
---|
1288 | return; |
---|
1289 | } |
---|
1290 | |
---|
1291 | if (n == 1) { |
---|
1292 | MulByX(c, a); |
---|
1293 | return; |
---|
1294 | } |
---|
1295 | |
---|
1296 | if (n < 0) { |
---|
1297 | if (n < -NTL_MAX_LONG) |
---|
1298 | clear(c); |
---|
1299 | else |
---|
1300 | RightShift(c, a, -n); |
---|
1301 | return; |
---|
1302 | } |
---|
1303 | |
---|
1304 | if (NTL_OVERFLOW(n, 1, 0)) |
---|
1305 | Error("overflow in LeftShift"); |
---|
1306 | |
---|
1307 | if (n == 0) { |
---|
1308 | c = a; |
---|
1309 | return; |
---|
1310 | } |
---|
1311 | |
---|
1312 | long sa = a.xrep.length(); |
---|
1313 | |
---|
1314 | long wn = n/NTL_BITS_PER_LONG; |
---|
1315 | long bn = n - wn*NTL_BITS_PER_LONG; |
---|
1316 | |
---|
1317 | long sc = sa + wn; |
---|
1318 | if (bn) sc++; |
---|
1319 | |
---|
1320 | c.xrep.SetLength(sc); |
---|
1321 | |
---|
1322 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1323 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1324 | |
---|
1325 | long i; |
---|
1326 | |
---|
1327 | if (bn == 0) { |
---|
1328 | for (i = sa+wn-1; i >= wn; i--) |
---|
1329 | cp[i] = ap[i-wn]; |
---|
1330 | for (i = wn-1; i >= 0; i--) |
---|
1331 | cp[i] = 0; |
---|
1332 | } |
---|
1333 | else { |
---|
1334 | cp[sa+wn] = ap[sa-1] >> (NTL_BITS_PER_LONG-bn); |
---|
1335 | for (i = sa+wn-1; i >= wn+1; i--) |
---|
1336 | cp[i] = (ap[i-wn] << bn) | (ap[i-wn-1] >> (NTL_BITS_PER_LONG-bn)); |
---|
1337 | cp[wn] = ap[0] << bn; |
---|
1338 | for (i = wn-1; i >= 0; i--) |
---|
1339 | cp[i] = 0; |
---|
1340 | } |
---|
1341 | |
---|
1342 | c.normalize(); |
---|
1343 | } |
---|
1344 | |
---|
1345 | void ShiftAdd(GF2X& c, const GF2X& a, long n) |
---|
1346 | // c = c + a*X^n |
---|
1347 | { |
---|
1348 | if (n < 0) Error("ShiftAdd: negative argument"); |
---|
1349 | |
---|
1350 | if (n == 0) { |
---|
1351 | add(c, c, a); |
---|
1352 | return; |
---|
1353 | } |
---|
1354 | |
---|
1355 | if (NTL_OVERFLOW(n, 1, 0)) |
---|
1356 | Error("overflow in ShiftAdd"); |
---|
1357 | |
---|
1358 | long sa = a.xrep.length(); |
---|
1359 | if (sa <= 0) { |
---|
1360 | return; |
---|
1361 | } |
---|
1362 | |
---|
1363 | long sc = c.xrep.length(); |
---|
1364 | |
---|
1365 | long wn = n/NTL_BITS_PER_LONG; |
---|
1366 | long bn = n - wn*NTL_BITS_PER_LONG; |
---|
1367 | |
---|
1368 | long ss = sa + wn; |
---|
1369 | if (bn) ss++; |
---|
1370 | |
---|
1371 | if (ss > sc) |
---|
1372 | c.xrep.SetLength(ss); |
---|
1373 | |
---|
1374 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1375 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1376 | |
---|
1377 | long i; |
---|
1378 | |
---|
1379 | for (i = sc; i < ss; i++) |
---|
1380 | cp[i] = 0; |
---|
1381 | |
---|
1382 | if (bn == 0) { |
---|
1383 | for (i = sa+wn-1; i >= wn; i--) |
---|
1384 | cp[i] ^= ap[i-wn]; |
---|
1385 | } |
---|
1386 | else { |
---|
1387 | cp[sa+wn] ^= ap[sa-1] >> (NTL_BITS_PER_LONG-bn); |
---|
1388 | for (i = sa+wn-1; i >= wn+1; i--) |
---|
1389 | cp[i] ^= (ap[i-wn] << bn) | (ap[i-wn-1] >> (NTL_BITS_PER_LONG-bn)); |
---|
1390 | cp[wn] ^= ap[0] << bn; |
---|
1391 | } |
---|
1392 | |
---|
1393 | c.normalize(); |
---|
1394 | } |
---|
1395 | |
---|
1396 | |
---|
1397 | |
---|
1398 | |
---|
1399 | void RightShift(GF2X& c, const GF2X& a, long n) |
---|
1400 | { |
---|
1401 | if (IsZero(a)) { |
---|
1402 | clear(c); |
---|
1403 | return; |
---|
1404 | } |
---|
1405 | |
---|
1406 | if (n < 0) { |
---|
1407 | if (n < -NTL_MAX_LONG) Error("overflow in RightShift"); |
---|
1408 | LeftShift(c, a, -n); |
---|
1409 | return; |
---|
1410 | } |
---|
1411 | |
---|
1412 | if (n == 0) { |
---|
1413 | c = a; |
---|
1414 | return; |
---|
1415 | } |
---|
1416 | |
---|
1417 | long sa = a.xrep.length(); |
---|
1418 | long wn = n/NTL_BITS_PER_LONG; |
---|
1419 | long bn = n - wn*NTL_BITS_PER_LONG; |
---|
1420 | |
---|
1421 | if (wn >= sa) { |
---|
1422 | clear(c); |
---|
1423 | return; |
---|
1424 | } |
---|
1425 | |
---|
1426 | c.xrep.SetLength(sa-wn); |
---|
1427 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1428 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1429 | |
---|
1430 | long i; |
---|
1431 | |
---|
1432 | if (bn == 0) { |
---|
1433 | for (i = 0; i < sa-wn; i++) |
---|
1434 | cp[i] = ap[i+wn]; |
---|
1435 | } |
---|
1436 | else { |
---|
1437 | for (i = 0; i < sa-wn-1; i++) |
---|
1438 | cp[i] = (ap[i+wn] >> bn) | (ap[i+wn+1] << (NTL_BITS_PER_LONG - bn)); |
---|
1439 | |
---|
1440 | cp[sa-wn-1] = ap[sa-1] >> bn; |
---|
1441 | } |
---|
1442 | |
---|
1443 | c.normalize(); |
---|
1444 | } |
---|
1445 | |
---|
1446 | |
---|
1447 | |
---|
1448 | static _ntl_ulong revtab[256] = { |
---|
1449 | |
---|
1450 | 0UL, 128UL, 64UL, 192UL, 32UL, 160UL, 96UL, 224UL, 16UL, 144UL, |
---|
1451 | 80UL, 208UL, 48UL, 176UL, 112UL, 240UL, 8UL, 136UL, 72UL, 200UL, |
---|
1452 | 40UL, 168UL, 104UL, 232UL, 24UL, 152UL, 88UL, 216UL, 56UL, 184UL, |
---|
1453 | 120UL, 248UL, 4UL, 132UL, 68UL, 196UL, 36UL, 164UL, 100UL, 228UL, |
---|
1454 | 20UL, 148UL, 84UL, 212UL, 52UL, 180UL, 116UL, 244UL, 12UL, 140UL, |
---|
1455 | 76UL, 204UL, 44UL, 172UL, 108UL, 236UL, 28UL, 156UL, 92UL, 220UL, |
---|
1456 | 60UL, 188UL, 124UL, 252UL, 2UL, 130UL, 66UL, 194UL, 34UL, 162UL, |
---|
1457 | 98UL, 226UL, 18UL, 146UL, 82UL, 210UL, 50UL, 178UL, 114UL, 242UL, |
---|
1458 | 10UL, 138UL, 74UL, 202UL, 42UL, 170UL, 106UL, 234UL, 26UL, 154UL, |
---|
1459 | 90UL, 218UL, 58UL, 186UL, 122UL, 250UL, 6UL, 134UL, 70UL, 198UL, |
---|
1460 | 38UL, 166UL, 102UL, 230UL, 22UL, 150UL, 86UL, 214UL, 54UL, 182UL, |
---|
1461 | 118UL, 246UL, 14UL, 142UL, 78UL, 206UL, 46UL, 174UL, 110UL, 238UL, |
---|
1462 | 30UL, 158UL, 94UL, 222UL, 62UL, 190UL, 126UL, 254UL, 1UL, 129UL, |
---|
1463 | 65UL, 193UL, 33UL, 161UL, 97UL, 225UL, 17UL, 145UL, 81UL, 209UL, |
---|
1464 | 49UL, 177UL, 113UL, 241UL, 9UL, 137UL, 73UL, 201UL, 41UL, 169UL, |
---|
1465 | 105UL, 233UL, 25UL, 153UL, 89UL, 217UL, 57UL, 185UL, 121UL, 249UL, |
---|
1466 | 5UL, 133UL, 69UL, 197UL, 37UL, 165UL, 101UL, 229UL, 21UL, 149UL, |
---|
1467 | 85UL, 213UL, 53UL, 181UL, 117UL, 245UL, 13UL, 141UL, 77UL, 205UL, |
---|
1468 | 45UL, 173UL, 109UL, 237UL, 29UL, 157UL, 93UL, 221UL, 61UL, 189UL, |
---|
1469 | 125UL, 253UL, 3UL, 131UL, 67UL, 195UL, 35UL, 163UL, 99UL, 227UL, |
---|
1470 | 19UL, 147UL, 83UL, 211UL, 51UL, 179UL, 115UL, 243UL, 11UL, 139UL, |
---|
1471 | 75UL, 203UL, 43UL, 171UL, 107UL, 235UL, 27UL, 155UL, 91UL, 219UL, |
---|
1472 | 59UL, 187UL, 123UL, 251UL, 7UL, 135UL, 71UL, 199UL, 39UL, 167UL, |
---|
1473 | 103UL, 231UL, 23UL, 151UL, 87UL, 215UL, 55UL, 183UL, 119UL, 247UL, |
---|
1474 | 15UL, 143UL, 79UL, 207UL, 47UL, 175UL, 111UL, 239UL, 31UL, 159UL, |
---|
1475 | 95UL, 223UL, 63UL, 191UL, 127UL, 255UL }; |
---|
1476 | |
---|
1477 | static inline |
---|
1478 | _ntl_ulong rev1(_ntl_ulong a) |
---|
1479 | { |
---|
1480 | return NTL_BB_REV_CODE; |
---|
1481 | } |
---|
1482 | |
---|
1483 | |
---|
1484 | |
---|
1485 | void CopyReverse(GF2X& c, const GF2X& a, long hi) |
---|
1486 | // c[0..hi] = reverse(a[0..hi]), with zero fill as necessary |
---|
1487 | // input may alias output |
---|
1488 | |
---|
1489 | { |
---|
1490 | if (hi < 0) { clear(c); return; } |
---|
1491 | |
---|
1492 | if (NTL_OVERFLOW(hi, 1, 0)) |
---|
1493 | Error("overflow in CopyReverse"); |
---|
1494 | |
---|
1495 | long n = hi+1; |
---|
1496 | long sa = a.xrep.length(); |
---|
1497 | if (n <= 0 || sa <= 0) { |
---|
1498 | clear(c); |
---|
1499 | return; |
---|
1500 | } |
---|
1501 | |
---|
1502 | long wn = n/NTL_BITS_PER_LONG; |
---|
1503 | long bn = n - wn*NTL_BITS_PER_LONG; |
---|
1504 | |
---|
1505 | if (bn != 0) { |
---|
1506 | wn++; |
---|
1507 | bn = NTL_BITS_PER_LONG - bn; |
---|
1508 | } |
---|
1509 | |
---|
1510 | c.xrep.SetLength(wn); |
---|
1511 | |
---|
1512 | _ntl_ulong *cp = c.xrep.elts(); |
---|
1513 | const _ntl_ulong *ap = a.xrep.elts(); |
---|
1514 | |
---|
1515 | long mm = min(sa, wn); |
---|
1516 | long i; |
---|
1517 | |
---|
1518 | for (i = 0; i < mm; i++) |
---|
1519 | cp[i] = ap[i]; |
---|
1520 | |
---|
1521 | for (i = mm; i < wn; i++) |
---|
1522 | cp[i] = 0; |
---|
1523 | |
---|
1524 | if (bn != 0) { |
---|
1525 | for (i = wn-1; i >= 1; i--) |
---|
1526 | cp[i] = (cp[i] << bn) | (cp[i-1] >> (NTL_BITS_PER_LONG-bn)); |
---|
1527 | cp[0] = cp[0] << bn; |
---|
1528 | } |
---|
1529 | |
---|
1530 | for (i = 0; i < wn/2; i++) { |
---|
1531 | _ntl_ulong t; t = cp[i]; cp[i] = cp[wn-1-i]; cp[wn-1-i] = t; |
---|
1532 | } |
---|
1533 | |
---|
1534 | for (i = 0; i < wn; i++) |
---|
1535 | cp[i] = rev1(cp[i]); |
---|
1536 | |
---|
1537 | c.normalize(); |
---|
1538 | } |
---|
1539 | |
---|
1540 | |
---|
1541 | void div(GF2X& q, const GF2X& a, GF2 b) |
---|
1542 | { |
---|
1543 | if (b == 0) |
---|
1544 | Error("div: division by zero"); |
---|
1545 | |
---|
1546 | q = a; |
---|
1547 | } |
---|
1548 | |
---|
1549 | void div(GF2X& q, const GF2X& a, long b) |
---|
1550 | { |
---|
1551 | if ((b & 1) == 0) |
---|
1552 | Error("div: division by zero"); |
---|
1553 | |
---|
1554 | q = a; |
---|
1555 | } |
---|
1556 | |
---|
1557 | |
---|
1558 | |
---|
1559 | void GF2XFromBytes(GF2X& x, const unsigned char *p, long n) |
---|
1560 | { |
---|
1561 | if (n <= 0) { |
---|
1562 | x = 0; |
---|
1563 | return; |
---|
1564 | } |
---|
1565 | |
---|
1566 | const long BytesPerLong = NTL_BITS_PER_LONG/8; |
---|
1567 | |
---|
1568 | long lw, r, i, j; |
---|
1569 | |
---|
1570 | lw = n/BytesPerLong; |
---|
1571 | r = n - lw*BytesPerLong; |
---|
1572 | |
---|
1573 | if (r != 0) |
---|
1574 | lw++; |
---|
1575 | else |
---|
1576 | r = BytesPerLong; |
---|
1577 | |
---|
1578 | x.xrep.SetLength(lw); |
---|
1579 | unsigned long *xp = x.xrep.elts(); |
---|
1580 | |
---|
1581 | for (i = 0; i < lw-1; i++) { |
---|
1582 | unsigned long t = 0; |
---|
1583 | for (j = 0; j < BytesPerLong; j++) { |
---|
1584 | t >>= 8; |
---|
1585 | t += (((unsigned long)(*p)) & 255UL) << ((BytesPerLong-1)*8); |
---|
1586 | p++; |
---|
1587 | } |
---|
1588 | xp[i] = t; |
---|
1589 | } |
---|
1590 | |
---|
1591 | unsigned long t = 0; |
---|
1592 | for (j = 0; j < r; j++) { |
---|
1593 | t >>= 8; |
---|
1594 | t += (((unsigned long)(*p)) & 255UL) << ((BytesPerLong-1)*8); |
---|
1595 | p++; |
---|
1596 | } |
---|
1597 | |
---|
1598 | t >>= (BytesPerLong-r)*8; |
---|
1599 | xp[lw-1] = t; |
---|
1600 | |
---|
1601 | x.normalize(); |
---|
1602 | } |
---|
1603 | |
---|
1604 | void BytesFromGF2X(unsigned char *p, const GF2X& a, long n) |
---|
1605 | { |
---|
1606 | if (n < 0) n = 0; |
---|
1607 | |
---|
1608 | const long BytesPerLong = NTL_BITS_PER_LONG/8; |
---|
1609 | |
---|
1610 | long lbits = deg(a) + 1; |
---|
1611 | long lbytes = (lbits+7)/8; |
---|
1612 | |
---|
1613 | long min_bytes = min(lbytes, n); |
---|
1614 | |
---|
1615 | long min_words = min_bytes/BytesPerLong; |
---|
1616 | long r = min_bytes - min_words*BytesPerLong; |
---|
1617 | if (r != 0) |
---|
1618 | min_words++; |
---|
1619 | else |
---|
1620 | r = BytesPerLong; |
---|
1621 | |
---|
1622 | const unsigned long *ap = a.xrep.elts(); |
---|
1623 | |
---|
1624 | long i, j; |
---|
1625 | |
---|
1626 | for (i = 0; i < min_words-1; i++) { |
---|
1627 | unsigned long t = ap[i]; |
---|
1628 | for (j = 0; j < BytesPerLong; j++) { |
---|
1629 | *p = t & 255UL; |
---|
1630 | t >>= 8; |
---|
1631 | p++; |
---|
1632 | } |
---|
1633 | } |
---|
1634 | |
---|
1635 | if (min_words > 0) { |
---|
1636 | unsigned long t = ap[min_words-1]; |
---|
1637 | for (j = 0; j < r; j++) { |
---|
1638 | *p = t & 255UL; |
---|
1639 | t >>= 8; |
---|
1640 | p++; |
---|
1641 | } |
---|
1642 | } |
---|
1643 | |
---|
1644 | for (j = min_bytes; j < n; j++) { |
---|
1645 | *p = 0; |
---|
1646 | p++; |
---|
1647 | } |
---|
1648 | } |
---|
1649 | |
---|
1650 | NTL_END_IMPL |
---|